Matt Walsh and Biblical arguments
Yes, Christians should use Scripture in arguments over public policy and cultural issues. Where there has been disagreement is the time and place to use such arguments, and what tools to use in addition to Scripture. Therefore, I understand the point Matt Walsh is making (see here and here and here) in terms of using secular arguments to convince unbelievers of our position. I also understand Walsh's critics on the issue. Unfortunately, I think Walsh has misunderstood the arguments made against his position.
Walsh has said that only using Scripture is ineffective for someone who rejects the authority of Scripture, and that we should also use the evidence, truth, and logic that God has enabled us to use by giving us the ability to think and reason. But I do not know of anyone who is saying that we should not use secular arguments at all. Walsh is knocking over a straw man by refuting an argument that no one is making. To be clear: I do not think Walsh was being dishonest. I think he did not understand the argument being presented, and that some of his critics were probably not making the point clear.
Of course we should use reason: The anti-abortion movement has made great progress in educating the public about the humanity of unborn babies and critics of "trans women" in sports have been effective in appealing to scientific facts about men being bigger, faster, stronger and more durable than women. Even the Apostle Paul uses secular reasoning in some of his epistles alongside arguments from Old Testament scriptures and New Covenant doctrine.
But to argue that we should not use Scripture at all is faithless. Hebrews 4:12 teaches us that Scripture is "quick, and powerful, and sharper than any twoedged sword." We know that the Bible is the very Word of God, preserved for us across time. There is no tool we can use with the power of Scripture, and we should have faith that God can change hearts and call souls to repentance and faith. Our God is infinite, and we are finite. I say this as someone who has repented of my own faithlessness, because at one time I believed we should never use Scripture in a secular argument. I was wrong then and Walsh is wrong now.